Optical bandpass filters typically isolate a narrow portion of the wavelength spectrum and have applications in a broad range of technologies, ranging from astronomy to DNA Analyzers to Paint Color Matching Systems. Several types of filters exist, including, but not limited to, Fabry-Perot and birefringent interference filters. The choice of a particular design of filter depends on the application requirements regarding factors such as bandwidth, field-of-view, aperture size, and tuning.
One useful optical bandpass filter is a birefringent interference filter. The birefringent interference filter was apparently invented by Bernard Lyot in 1933 and later independently by Ohman who apparently constructed the first such filter to be used for solar observations.
Birefringent materials have the property that their index of refraction varies along different axis of a crystal or other material. Such materials are said to be anisotropic. The velocity of propagation of light is inversely proportional to the index of refraction, so that light passing along different orientations of the crystal material may travel at different velocities and will typically emerge phase-shifted. The crystal axis having the extraordinary refractive index is sometimes referred to as the Z axis of the birefingement material and sometimes simply as the optical axis of the material.
FIG. 1 is a schematic 3-D view of a birefringent material 11 acting as a half-wave retarder 10. When suitably oriented, the birefringent material 11 may have a first axis 16 having a first refractive index that allows a component of electromagnetic radiation 18 oriented parallel to that axis to travel faster than a component of electromagnetic radiation 14 that is parallel to a second axis 15 having a second refractive index and that is orthogonal to the first axis 16. The total length of the birefringent material 11 may be selected such that a component of electromagnetic radiation 14 parallel to the slow axis may be retarded by half a wavelength with respect to a component of electromagnetic radiation 18 oriented parallel to the fast axis 16. Electromagnetic radiation oriented at +45 degrees 12 with respect to the first axis 16 will, therefore, become oriented at −45 degrees 13 with respect to the first axis 16.
The birefringent material 11 of the appropriate length and crystalline orientation may, therefore, be used as a half wave retardation plate that transforms linear polarized electromagnetic radiation oriented at 45 degrees 12 with respect to the first axis 16 to linear polarized electromagnetic radiation oriented at −45 degrees with respect to the first axis 16.
FIG. 2 is a schematic representation of a half-wave retarder. An input linear polarizer 22 oriented at +45 degrees to the vertical is represented by a double arrow with the angle of orientation underneath. The half-wave retarder 10 is represented by a box with the value of the retardation at the top and the orientation of the fast axis with respect to the vertical at the bottom. An output linear polarizer 20 oriented at −45 degrees to the vertical is represented by a double arrow with the angle of orientation underneath.
FIG. 3 is a graph representing the spectral through put of a typical half-wave retarder 10. The vertical axis 26 represents the amount of light transmitted and the horizontal axis 28 represents the wavelength of the light. The phase shift Γ is wavelength dependent and may be represented mathematically as:Γ=2π.Δ.n.d/λwhere Δn is the birefringence that is equal to the difference between the ordinary and extraordinary indices of the material being used, i.e., Δn=ne−no, d is the length of the birefringent material 11, and λ is the wavelength of the light.
A wavelength phase shift that is an even integer multiple of π will result in maximum transmission through the half-wave retarder 10 of FIGS. 1 and 2, i.e., Γ=2mπ, where m is an integer, results in maximum transmission. A wavelength phase shift that is an odd integer multiple of π will result in a minimum transmission through the half-wave retarder 10 of FIGS. 1 and 2, i.e., Γ=(2m+1)π, where m is an integer, results in maximum transmission. The normalized intensity may, therefore, be represented by the mathematical equation:I=cos2(Γ/2)where Γ is the phase shift and at normal incidence as discussed above. This relationship between intensity and wavelength is represented graphically in FIG. 3.
This cyclic variation in transmission may be used to produce a narrow band filter by combining two or more half-wave retarder stages each having a crystal thickness that is twice that of the preceding stage, i.e., the thickness ratios of the stages are 1:2:4:8. In this way, every other maximum in transmission spectrum of the thickest stage may be suppressed by a minimum of the next thinnest stage.
FIG. 4 is a schematic representation of a two stage Lyot optical filter 40. An input linear polarizer 32 may be oriented so as to produce linear polarized light that is oriented vertically. A first stage birefringent element 30 of the two stage Lyot optical filter 40 may have a length that provides a retardation of 2mπ radians, where m is an integer. A second stage birefringent element 36 may be selected to be half the length of the first stage birefringent element 30 and therefore only provide half the retardation, i.e., mπ radians of retardation. A first linear polarizer 32, a second linear polarizer 34 and a third linear polarizer 38 may be all oriented to allow maximum transmission of vertically oriented polarized light.
FIG. 5 is a graphical representation of the spectral through put the two stage Lyot optical filter of FIG. 4. The spectral throughput of the thinner, second stage birefringent element 36 and the second linear polarizer 34 and the linear polarizer 38 is represented by the dotted line curve 42. The spectral throughput of the thicker, first stage birefringent element 30 is represented by the dotted line curve 44. The combined spectral throughput of all the optical elements of the two stage Lyot optical filter 40 is represented by a solid line curve 46. As the solid line curve 46 indicates, even the two stage Lyot optical filter 40 is capable of isolating a relatively narrow band of electromagnetic radiation.
In order to isolate an even narrower bandwidth of the spectrum, more stages may be added to the filter. A practical problem is that as all stages have to transmit the wavelength being isolated. All the stages, therefore, ought to have a maximum of transmission at that wavelength, else the total transmission through the filter will be impaired. To avoid having to have unduly strict manufacturing tolerances on the optical elements, it is possible to insert elements with a tunable retardation, such as a liquid crystal element, into each stage of the filter, though this has the disadvantage of introducing adding additional elements. Minimizing the number of elements in an optical filter is usually desirable. It would, therefore, be highly advantageous to produce a stage of a Lyot filter that is easily tunable without the need for additional elements.